Radar-operated vehicle safety systems provide a collision warning signal when the vehicle is in danger of collision by comparing the detected range to the object with an estimated vehicle's stopping distance. Because of the space limitations, the size of an antenna mounted on the vehicle is desired to be as small as possible, which contradicts with the desire to obtain a narrow beam width since such a narrow beam is only possible with the use of a parabolic antenna too large for mounting on the vehicle. The resultant radar beam would thus disperse to such a degree that echo signals from fixed targets along the roadway or from oncoming vehicles on different lanes produce invalid warning signals.
It has been proposed to utilize the fact that the angular displacement of a target increases inversely with the distance thereto. A range of angular displacements is determined as a function of the distance to the target and used to discard the signals that return from targets outside of the predetermined range.
Japanese Patent Application No. Sho 51-21803 discloses a radar-operated safety system which senses a number of input variables and if the following conditions are simultaneously met, the system recognizes that the vehicle is in danger or collision and issues a warning signal that is used to alert the driver or operate brakes: ##EQU1## EQU R .gtoreq. Ra
where,
.theta. = angular displacement of the object from the center axis of the vehicle; PA1 R = detected distance to the object; PA1 Ra = stopping distance of the vehicle; PA1 Ra = Va.sup.2 /2.alpha., wherein Va .div. Vr (i.e. the object is stationary), or PA1 = Vr (2Va - Vr)/2.alpha., when Va is greater than Vr,
L = DISTANCE BETWEEN THE OBJECT AND THE CENTER AXIS OF THE VEHICLE;
where the stopping distance Ra is given by
where Va is the vehicle speed, .alpha., the amount of deceleration, and Vr, the vehicle speed relative to the object.